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On Koornwinder classical orthogonal polynomials in two variables

✍ Scribed by Lidia Fernández; Teresa E. Pérez; Miguel A. Piñar

Book ID
113511747
Publisher
Elsevier Science
Year
2012
Tongue
English
Weight
228 KB
Volume
236
Category
Article
ISSN
0377-0427

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Let for a, j?, y > -1, a+y+3/2 > 0, /l+y+3/2 > 0 and n > k > 0 the orthogonal polynomials pE:fy( u, V) be defined as polynomials in u and o with "highest" term un-kvX which are obtained by orthogonalization of the sequence 1, u, V, uz, uw, ~2, us, u2u, . . . with respect to the weight function (1 -u

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Let the region S={(x, y)I,u(x+iy, x-iy) >0) be the interior of Steiner's hypocycloid, where µ(z, z)=-z 222 +4z 3 +423-l8z2+27 . For each real a>-5/6 an orthogonal system of polynomials p.. n(z, z), m, n>0, can be defined on this region S such that pm,n (z, z)-zmzn has degree less than m+n and ff pr,